Di Maria, now at City's local rivals Manchester United, cost the Red Devils a British record fee of £59.7m in August earlier this year.
"We had important restrictions about our budget this year. We cannot spend the money that United paid for Di Maria," Pellegrini told reporters.
"We had important restrictions on the amount of players we can have this year and also the amount of money we can spend."
The former Real Madrid and Benfica winger will likely feature for the Red Devils as they come up against City in the Manchester derby this Sunday.